How do analogies relieve you to read between the lines a quantifiable problem?
Answer:
They relate something you don't understand (a trial concept, for example) to something you have more experience beside (what the problem is compared to).
For example: Do you understand what is expected when physicists say the universe itself is expanding? Can you picture it expanding ("expanding into what?" you might ask)? Probably not. But you can probably picture what it would look close to to draw a few dots on a balloon, and then blow the balloon up. All the points go and get farther away from each other, and nonetheless that new space between them seem to have come from nowhere. Note: the 2D surface of the balloon is designed to represent our 3D universe. The points you drew were celestial bodies (stars, galaxies, nebulae...).
An central thing to remember around analogies is that they are imperfect. You hold to know where they break down. In the balloon-universe example, the hot "space" on the balloon is just a result of the springy property of the rubber that was already at hand. There is nothing analogous to the rubber within the universe.
They substitute a simple problem that needs indistinguishable principles as the original problem to solve.
I intuitively think it's because adjectives science comes down to math, and analogies are the way we amount out the really hard math problems. But that's of late my own opinion.